NPS analysis
NPS - Comment analysis
In an [previous post](https://nitinahuja.github.io/2017/nps-exploratory-analysis-in-r/) we performed some EDA on the NPS data we have. Recall that as part of the question about the likelihood of recommending a service or business there is an optional text response about why they picked this score.
Let’s try and see what those responses are all about. We had already performed some sentiment analysis on this text we are now going to attempt to classify this text into topics. Topic modeling is a method for unsupervised classification of such documents, similar to clustering on numeric data, which finds natural groups of items even when we’re not sure what we’re looking for.
Latent Dirichlet allocation (LDA) is a particularly popular method for fitting a topic model. It treats each document as a mixture of topics, and each topic as a mixture of words.
LDA has two key tenets
- Every document is a mixture of topics
- Every topic is a mixture of words.
In our NPS comment data, we will treat each comment as a document and we’ll try and see how many topics we can identify. Since LDA is unsupervised classification, and we do not have any a priori knowledge of the possible number of topics, we’ll need to do some trial and error.
Let’s start by loading the required libraries
library(irlba)
library(tidytext)
library(topicmodels)
library(ggplot2)
library(tidyr)
library(dplyr)
library(RColorBrewer)
library(lubridate)
library(stringr)
library(widyr)
library(broom)
library(tidygraph)
library(ggraph)
library(ggrepel)
LDA needs a term document matrix, let’s start by reading in the data and remove the rows that do not have any comments.
nps <- read.csv('~/data/nps.csv', header = TRUE, quote = '"'
, na.strings=c("", "NA", "#N/A")
, colClasses = c("Feedback.Received"= "Date"
, "Comment"="character"
, "Survey.Sent"="Date"
, "TPY"="integer"
))
nps<- nps %>% drop_na(Comment)
That leaves us with 1130 rows.
Let’s also enrich the data with some additional fields and add the category like we did in the last post. The category is dependent on the score and scores from 0 through 6 are considered detractors, 7 - 8 are passives and 9 and 10 are promorters.
nps$year <- as.factor(year(nps$Received))
nps$month <- cut(nps$Received, breaks = "month")
nps$days <- nps$Received - nps$Sent
nps$weekday <- weekdays(nps$Received)
nps$weekday <- factor(nps$weekday, levels = c("Sunday", "Monday","Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"))
nps$cat <- cut(nps$Score, breaks = c(-1,6,8,10), labels = c("Detractor", "Passive", "Promoter"))
Extract out the comments while keeping the category
comments <- nps %>%
select(Comment, cat) %>%
group_by(row_number())
LDA using per comment as a document
The LDA function takes a TermDocumentMatrix object as an input; let’s convert our text into a DFM
nps_count <- comments %>%
unnest_tokens(word, Comment) %>%
anti_join(stop_words, by = c('word')) %>%
count(`row_number()`, word, sort = TRUE) %>%
ungroup()
Now convert to a DTM and perform the LDA
nps_dtm <- nps_count %>%
cast_dtm(`row_number()`, word, n)
LDA on the matrix. This produces a row per topic with each word and its probability of the word being generated by that topic. We picked seven topics but we will experiment with a few more combinations.
topic_count <- 25
nps_lda <- LDA(nps_dtm, k = topic_count, control = list(seed=1234))
nps_topics <- tidy(nps_lda, matrix = "beta")
Next - let’s find out the top 5 words per topic and plot those.
top_terms <- nps_topics %>%
group_by(topic) %>%
top_n(5, beta) %>%
ungroup() %>%
arrange(topic, -beta)
Plot the terms and topics.
top_terms %>%
mutate(term = reorder(term, beta)) %>%
ggplot(aes(term, beta, fill=factor(topic))) +
geom_col(show.legend = FALSE) +
facet_wrap(~ topic, scales = "free" ) +
coord_flip() +
guides(fill=FALSE) +
labs(title = "Terms in topics - By Comment", x = "Term", y = "Probability")
## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
In this model, we treated each comment as it’s own document and picked 20 topics to classify the text, we assume that each responder roughly commented across the same 20 topics; how does this change if we treat each category as it’s own document. Are respondents per category talking about the same topics.
LDA By Category
There are three categories and we will try to classify the text into three topics but this time let’s try to use bigrams for this.
nps_count <- comments %>%
ungroup() %>%
unnest_tokens(word ,Comment, token = "ngrams", n = 2) %>%
count(cat, word, sort = TRUE) %>%
ungroup()
Now convert to a DTM and perform the LDA
nps_dtm <- nps_count %>%
cast_dtm(cat, word, n)
*LDA on the matrix. *
This produces a row per topic with each word and its probability of the word being generated by that topic. We picked three topics but we will experiment with a few more combinations.
nps_lda <- LDA(nps_dtm, k = 3, control = list(seed=1234))
nps_topics <- tidy(nps_lda, matrix = "beta")
Next - let’s find out the top words per topic and plot those.
top_terms <- nps_topics %>%
group_by(topic) %>%
top_n(10, beta) %>%
ungroup() %>%
arrange(topic, -beta)
Plot the bigrams and topics; looking at the top terms, these seem to map well to the three categories - Promoters, Passives and detractors as 1, 2 and 3 respectively.
top_terms %>%
mutate(term = reorder(term, beta)) %>%
ggplot(aes(term, beta, fill=factor(topic))) +
geom_col(show.legend = FALSE) +
facet_wrap( ~ topic, scales = "free" ) +
coord_flip() +
guides(fill=FALSE) +
labs(title = "Bigrams in topics - By Category", x = "Term", y = "Probability")
## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
LDA can also model each document as a mixture of topics. We can examine the per-document-per-topic probabilities, called Y (“gamma”), with the matrix = “gamma” argument to tidy()
nps_docs <- tidy(nps_lda, matrix = "gamma")
nps_docs
## # A tibble: 9 × 3
## document topic gamma
## <chr> <int> <dbl>
## 1 Detractor 1 0.00000351
## 2 Passive 1 0.00000485
## 3 Promoter 1 1.00
## 4 Detractor 2 0.00000351
## 5 Passive 2 1.00
## 6 Promoter 2 0.00000417
## 7 Detractor 3 1.00
## 8 Passive 3 0.00000485
## 9 Promoter 3 0.00000417
Each of these values is an estimated proportion of words from that document that are generated from that topic. This confirms what we suspected - that topic 1 words were almost entirely (99%) generated of words from the promoters sections and topic 2’s words were generated from the passive documents.
Zipf’s Law
Let’s take a short detour before moving ahead. George Zipf, in the 1940’s, by hand took all the words in Ulysses and found that the frequency of a word was inversely proportinal to it’s rank. This observation applies to many phenomenon, including populations in cities.
nps_count <- nps %>%
select(Comment, cat) %>%
unnest_tokens(word, Comment) %>%
count(cat, word, sort = TRUE) %>%
ungroup()
cat_count <- nps_count %>%
group_by(cat) %>%
summarise( total = sum(n))
nps_count <- left_join(nps_count, cat_count, by = 'cat')
freq_by_rank <- nps_count %>%
group_by(cat) %>%
mutate(rank = row_number(), freq = n/total)
Now let’s plot the log-log plot for the rank and frequency.
freq_by_rank %>%
ggplot(aes(rank, freq, color = cat)) +
geom_line() +
scale_x_log10() +
scale_y_log10() +
scale_fill_brewer("category", palette = "Set1") +
labs(title = "Zipf's law")
It’s quite amazing to see that even a fragmented set of comments follows Zipf’s law. The slope is not quite -1 but close. We can find out what the linear fit is. Really close to -1.
lm(log10(freq) ~ log10(rank), data = freq_by_rank %>% filter(rank > 10))
##
## Call:
## lm(formula = log10(freq) ~ log10(rank), data = freq_by_rank %>%
## filter(rank > 10))
##
## Coefficients:
## (Intercept) log10(rank)
## -0.7715 -1.0264
Word Vectors
Word vectors are typically calculated using neural networks; that is what word2vec is. We will try to find word vectors in our own collection using some linear algebra. A lot of this is influenced by the excellent post by Julia Silge
We’ll start by counting unigram probabilities
comments <- nps %>%
select(Comment, cat) %>%
mutate(docID = row_number())
unigram_probs <- comments %>%
unnest_tokens(word, Comment) %>%
count(word, sort = TRUE) %>%
mutate(p = n /sum(n))
unigram_probs
## word n p
## 1 the 913 3.785084e-02
## 2 to 881 3.652419e-02
## 3 and 843 3.494880e-02
## 4 of 523 2.168235e-02
## 5 is 503 2.085320e-02
## 6 a 481 1.994113e-02
## 7 i 418 1.732930e-02
## 8 for 367 1.521496e-02
## 9 it 312 1.293479e-02
## 10 we 301 1.247875e-02
## 11 have 293 1.214709e-02
## 12 service 280 1.160814e-02
## 13 use 274 1.135940e-02
## 14 that 268 1.111065e-02
## 15 with 264 1.094482e-02
## 16 are 242 1.003275e-02
## 17 customer 229 9.493802e-03
## 18 our 225 9.327971e-03
## 19 in 211 8.747564e-03
## 20 not 209 8.664649e-03
## 21 great 201 8.332988e-03
## 22 system 191 7.918411e-03
## 23 support 187 7.752581e-03
## 24 easy 155 6.425936e-03
## 25 be 154 6.384478e-03
## 26 but 143 5.928444e-03
## 27 ease 142 5.886986e-03
## 28 on 137 5.679698e-03
## 29 very 134 5.555325e-03
## 30 there 125 5.182206e-03
## 31 you 120 4.974918e-03
## 32 would 118 4.892003e-03
## 33 been 114 4.726172e-03
## 34 as 112 4.643257e-03
## 35 like 112 4.643257e-03
## 36 has 104 4.311596e-03
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## 38 when 93 3.855562e-03
## 39 ticket 91 3.772646e-03
## 40 friendly 89 3.689731e-03
## 41 good 89 3.689731e-03
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## 43 my 82 3.399527e-03
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## 202 1 18 7.462377e-04
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## 219 doesn't 17 7.047801e-04
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## 227 think 17 7.047801e-04
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Next we will calculate the skipgram probabilities, how often we find a word near another word. To do this we will create a sliding window of words around a word and then use pairwise_count to count cooccuring pairs within each sliding window. Essentially we will be doing this P(word1, word2) /P(word1)/ P(word2). We’ll take a window of 8 words for each sliding window. I reached this number after some experimentation.
skipgrams <- comments %>%
unnest_tokens(ngram, Comment, token = "ngrams", n = 8) %>%
mutate(ngramID = row_number()) %>%
unite(skipgramID, docID, ngramID) %>%
unnest_tokens(word, ngram)
Next we do a pairwise count of the terms and find the relative probabilities.
skipgram_probs <- skipgrams %>%
pairwise_count(word, skipgramID, sort = TRUE, diag = TRUE) %>%
mutate(p = n /sum(n))
Normalized skipgram probability
normalized_prob <- skipgram_probs %>%
filter(n > 20) %>%
rename(word1 = item1, word2 = item2) %>%
left_join(unigram_probs %>%
select(word1 = word, p1 = p),
by = "word1") %>%
left_join(unigram_probs %>%
select(word2 = word, p2 = p),
by = "word2") %>%
mutate(p_together = p / p1 / p2)
Just with this information we can try and find some word associations - which words are most closely associated with service
normalized_prob %>%
filter(word1 == "service") %>%
arrange(-p_together)
## # A tibble: 39 × 7
## word1 word2 n p p1 p2 p_together
## <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 service service 718 0.000675 0.0116 0.0116 5.01
## 2 service customer 336 0.000316 0.0116 0.00949 2.87
## 3 service excellent 37 0.0000348 0.0116 0.00153 1.95
## 4 service their 25 0.0000235 0.0116 0.00149 1.36
## 5 service product 40 0.0000376 0.0116 0.00269 1.20
## 6 service great 116 0.000109 0.0116 0.00833 1.13
## 7 service good 48 0.0000451 0.0116 0.00369 1.05
## 8 service your 49 0.0000460 0.0116 0.00398 0.997
## 9 service but 66 0.0000620 0.0116 0.00593 0.901
## 10 service get 25 0.0000235 0.0116 0.00257 0.787
## # ℹ 29 more rows
How about customer
normalized_prob %>%
filter(word1 == "customer") %>%
arrange(-p_together)
## # A tibble: 31 × 7
## word1 word2 n p p1 p2 p_together
## <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 customer customer 588 0.000553 0.00949 0.00949 6.13
## 2 customer service 336 0.000316 0.00949 0.0116 2.87
## 3 customer by 22 0.0000207 0.00949 0.00108 2.02
## 4 customer excellent 25 0.0000235 0.00949 0.00153 1.61
## 5 customer support 109 0.000102 0.00949 0.00775 1.39
## 6 customer great 78 0.0000733 0.00949 0.00833 0.927
## 7 customer good 31 0.0000291 0.00949 0.00369 0.832
## 8 customer very 43 0.0000404 0.00949 0.00556 0.766
## 9 customer friendly 24 0.0000226 0.00949 0.00369 0.644
## 10 customer and 208 0.000195 0.00949 0.0349 0.589
## # ℹ 21 more rows
How about the negative qualifier not
normalized_prob %>%
filter(word1 == "not") %>%
arrange(-p_together)
## # A tibble: 79 × 7
## word1 word2 n p p1 p2 p_together
## <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 not not 1314 0.00123 0.00866 0.00866 16.4
## 2 not did 50 0.0000470 0.00866 0.000497 10.9
## 3 not sure 26 0.0000244 0.00866 0.000332 8.50
## 4 not enough 23 0.0000216 0.00866 0.000332 7.52
## 5 not does 56 0.0000526 0.00866 0.000829 7.33
## 6 not fixed 26 0.0000244 0.00866 0.000415 6.80
## 7 not flexible 27 0.0000254 0.00866 0.000497 5.89
## 8 not i'm 32 0.0000301 0.00866 0.000663 5.23
## 9 not may 23 0.0000216 0.00866 0.000497 5.01
## 10 not perfect 41 0.0000385 0.00866 0.000912 4.88
## # ℹ 69 more rows
Next we want to perform matrix factorization, cast to a matrix. This produces a matrix of m x m size with most of values being 0.
pmi_matrix <- normalized_prob %>%
mutate(pmi = log10(p_together)) %>%
cast_sparse(word1, word2, pmi)
Next, produce a sparse matrix to reduce dimesionality.
pmi_svd <- irlba(pmi_matrix, 256, maxit = 1e3)
Next we get the word vectors
word_vectors <- pmi_svd$u
rownames(word_vectors) <- rownames(pmi_matrix)
Here is function to tidy the output
search_synonyms <- function(word_vectors, selected_vector) {
similarities <- word_vectors * selected_vector %>%
tidy() %>%
as_tibble() %>%
rename(token = .rownames,
similarity = unrowname.x.)
similarities %>%
arrange(-similarity)
}
Graph Analysis
Next, we will look at the bigrams again, but this time create a graph of co-occuence and other similar graph operations. Start by creating bigrams and creating a graph of linked words.
bigram_graph <- comments %>%
unnest_tokens(bigram ,Comment, token = "ngrams", n = 2) %>%
separate(bigram, c("word1", "word2"), sep = " " ) %>%
anti_join(stop_words, by = c("word1" = "word")) %>%
anti_join(stop_words, by = c("word2" = "word")) %>%
group_by(cat) %>%
count(word1, word2, sort = TRUE) %>%
select(word1, word2, cat, n) %>%
filter(n>2) %>%
as_tbl_graph()
## Warning in graph_from_data_frame(x, directed = directed): In `d' `NA' elements
## were replaced with string "NA"
Now let’s plot out the central themes here.
Centrality of words
bigram_graph %>%
mutate(centrality = centrality_degree()) %>%
ggraph(layout = 'kk') +
geom_edge_link() +
geom_node_point(aes(size = centrality, color = centrality)) +
geom_node_text(aes(label = name), repel = TRUE) +
theme_graph() +
theme(legend.position = "none")
## Warning: Using the `size` aesthetic in this geom was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` in the `default_aes` field and elsewhere instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
Clusters
bigram_graph %>%
mutate(community = as.factor(group_infomap())) %>%
ggraph(layout = 'kk') +
geom_edge_link(aes(alpha = ..index..), show.legend = FALSE) +
geom_node_point(aes(colour = community), size = 5) +
geom_node_text(aes(label = name), repel = TRUE) +
theme_graph()
## Warning: The dot-dot notation (`..index..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(index)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
Final Thoughts
In these two posts we explored NPS quite deeply. We saw that the score had moved up consistently over the years, we saw that respondents clearly gave higher scores on certain days of the week, the platform is serving certain types of business better than others, comments are generally positive and customer service is loved accross the board but is also blamed for system shortcomings. We had a limted corpus of comments and having more would have helped with LDA and topic modeling.
